A group of boys and girls is in a room. 5 girls leave the room, and the remaining group is in a ratio of boys to girls that is equal to 3:2. After this, 12 boys leave the room, and the remaining group is in a ratio of boys to girls that is equal to 3:4. Before all the departures, how many boys and how many girls were in the room?
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Let the number of boys = x
Let the number of girls = y
5 girls leave
x /( y-5) = 3/2
2x = 3y - 15
2x - 3y = -15 ------ (1)
12 boys leave
(x -12)/(y - 5) = 3/4
4x - 3y = 33 ----------- (ii)
Subtract (i) from (ii)
2x = 48
x = 24
2x - 3y = -15
2(24) - 3y = -5
48 - 3y = -15
-3y = -63
y = 21
The number of boys was 24
The number of girls was 21
Let the number of girls = y
5 girls leave
x /( y-5) = 3/2
2x = 3y - 15
2x - 3y = -15 ------ (1)
12 boys leave
(x -12)/(y - 5) = 3/4
4x - 3y = 33 ----------- (ii)
Subtract (i) from (ii)
2x = 48
x = 24
2x - 3y = -15
2(24) - 3y = -5
48 - 3y = -15
-3y = -63
y = 21
The number of boys was 24
The number of girls was 21
Answered by
0
Answer:
Step-by-step explanation:
Let the number of boys = x
Let the number of girls = y
5 girls leave
x /( y-5) = 3/2
2x = 3y - 15
2x - 3y = -15 ------ (1)
12 boys leave
(x -12)/(y - 5) = 3/4
4x - 3y = 33 ----------- (ii)
Subtract (i) from (ii)
2x = 48
x = 24
2x - 3y = -15
2(24) - 3y = -5
48 - 3y = -15
-3y = -63
y = 21
The number of boys was 24
The number of girls was 21
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